{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:2Q56MYFYYILHTWW4NAZHLCAVAR","short_pith_number":"pith:2Q56MYFY","canonical_record":{"source":{"id":"1010.4120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-20T08:08:33Z","cross_cats_sorted":["cond-mat.stat-mech","physics.chem-ph"],"title_canon_sha256":"d5618822460220755b1cf84651943df2c62877c55d094dfa67e2452f92a93ac4","abstract_canon_sha256":"f63880e352eea4559c194089c1c8da3e30bff5ca446288de4cf497b550d3c4f5"},"schema_version":"1.0"},"canonical_sha256":"d43be660b8c21679dadc6832758815044f2055d64e9e1a22ea66b7c71219b1ae","source":{"kind":"arxiv","id":"1010.4120","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4120","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4120v2","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4120","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"2Q56MYFYYILH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2Q56MYFYYILHTWW4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2Q56MYFY","created_at":"2026-05-18T12:26:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:2Q56MYFYYILHTWW4NAZHLCAVAR","target":"record","payload":{"canonical_record":{"source":{"id":"1010.4120","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-20T08:08:33Z","cross_cats_sorted":["cond-mat.stat-mech","physics.chem-ph"],"title_canon_sha256":"d5618822460220755b1cf84651943df2c62877c55d094dfa67e2452f92a93ac4","abstract_canon_sha256":"f63880e352eea4559c194089c1c8da3e30bff5ca446288de4cf497b550d3c4f5"},"schema_version":"1.0"},"canonical_sha256":"d43be660b8c21679dadc6832758815044f2055d64e9e1a22ea66b7c71219b1ae","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:23:45.216283Z","signature_b64":"SbdbgI9JPB12QrDuNuYz6rVIG2ag45tdtRqP7iX5/hA8R0TJ7yypBnvxRcvkUr2IQ0Oz+EAh7LOlIjhMxSQyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d43be660b8c21679dadc6832758815044f2055d64e9e1a22ea66b7c71219b1ae","last_reissued_at":"2026-05-18T02:23:45.215627Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:23:45.215627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1010.4120","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"KvUIB2vXZ13Hmn3tkLrFPEhZL4T/dzcJkHNugAf1TpQYUJ5fntHz7HvCV/PjBc28Nh/XkQUnHKDK2auyLLbbBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:57:00.304893Z"},"content_sha256":"39b05486a5a91ba18ab9e6bf73a6e54ca4bca4f75b16c7e46240983a5f22def3","schema_version":"1.0","event_id":"sha256:39b05486a5a91ba18ab9e6bf73a6e54ca4bca4f75b16c7e46240983a5f22def3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:2Q56MYFYYILHTWW4NAZHLCAVAR","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Multicomponent fluids of hard hyperspheres in odd dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.stat-mech","physics.chem-ph"],"primary_cat":"cond-mat.soft","authors_text":"Andr\\'es Santos, Ren\\'e D. Rohrmann","submitted_at":"2010-10-20T08:08:33Z","abstract_excerpt":"Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlations functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein--Zernike equation coupled with the Percus--Yevick closure, thus extending to arbitrary odd dimension the sol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4120","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:23:45Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"E1B7cjf99UD37O2+SH8ayvFn41axUkoRZyLNr5nDNHV54OlewWXvylIfqsfCHYBqkRX7/yMVWIp6yTKCQsQCDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-28T02:57:00.305245Z"},"content_sha256":"7fde5ab4c8f4042efcccdc0ad231958fd77d537861ef3672a25fc08ef7fa76e9","schema_version":"1.0","event_id":"sha256:7fde5ab4c8f4042efcccdc0ad231958fd77d537861ef3672a25fc08ef7fa76e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/bundle.json","state_url":"https://pith.science/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-05-28T02:57:00Z","links":{"resolver":"https://pith.science/pith/2Q56MYFYYILHTWW4NAZHLCAVAR","bundle":"https://pith.science/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/bundle.json","state":"https://pith.science/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2Q56MYFYYILHTWW4NAZHLCAVAR/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:2Q56MYFYYILHTWW4NAZHLCAVAR","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f63880e352eea4559c194089c1c8da3e30bff5ca446288de4cf497b550d3c4f5","cross_cats_sorted":["cond-mat.stat-mech","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-20T08:08:33Z","title_canon_sha256":"d5618822460220755b1cf84651943df2c62877c55d094dfa67e2452f92a93ac4"},"schema_version":"1.0","source":{"id":"1010.4120","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1010.4120","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"arxiv_version","alias_value":"1010.4120v2","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1010.4120","created_at":"2026-05-18T02:23:45Z"},{"alias_kind":"pith_short_12","alias_value":"2Q56MYFYYILH","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_16","alias_value":"2Q56MYFYYILHTWW4","created_at":"2026-05-18T12:26:03Z"},{"alias_kind":"pith_short_8","alias_value":"2Q56MYFY","created_at":"2026-05-18T12:26:03Z"}],"graph_snapshots":[{"event_id":"sha256:7fde5ab4c8f4042efcccdc0ad231958fd77d537861ef3672a25fc08ef7fa76e9","target":"graph","created_at":"2026-05-18T02:23:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Mixtures of hard hyperspheres in odd space dimensionalities are studied with an analytical approximation method. This technique is based on the so-called Rational Function Approximation and provides a procedure for evaluating equations of state, structure factors, radial distribution functions, and direct correlations functions of additive mixtures of hard hyperspheres with any number of components and in arbitrary odd-dimension space. The method gives the exact solution of the Ornstein--Zernike equation coupled with the Percus--Yevick closure, thus extending to arbitrary odd dimension the sol","authors_text":"Andr\\'es Santos, Ren\\'e D. Rohrmann","cross_cats":["cond-mat.stat-mech","physics.chem-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-20T08:08:33Z","title":"Multicomponent fluids of hard hyperspheres in odd dimensions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.4120","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:39b05486a5a91ba18ab9e6bf73a6e54ca4bca4f75b16c7e46240983a5f22def3","target":"record","created_at":"2026-05-18T02:23:45Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f63880e352eea4559c194089c1c8da3e30bff5ca446288de4cf497b550d3c4f5","cross_cats_sorted":["cond-mat.stat-mech","physics.chem-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"cond-mat.soft","submitted_at":"2010-10-20T08:08:33Z","title_canon_sha256":"d5618822460220755b1cf84651943df2c62877c55d094dfa67e2452f92a93ac4"},"schema_version":"1.0","source":{"id":"1010.4120","kind":"arxiv","version":2}},"canonical_sha256":"d43be660b8c21679dadc6832758815044f2055d64e9e1a22ea66b7c71219b1ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d43be660b8c21679dadc6832758815044f2055d64e9e1a22ea66b7c71219b1ae","first_computed_at":"2026-05-18T02:23:45.215627Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:23:45.215627Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SbdbgI9JPB12QrDuNuYz6rVIG2ag45tdtRqP7iX5/hA8R0TJ7yypBnvxRcvkUr2IQ0Oz+EAh7LOlIjhMxSQyDg==","signature_status":"signed_v1","signed_at":"2026-05-18T02:23:45.216283Z","signed_message":"canonical_sha256_bytes"},"source_id":"1010.4120","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:39b05486a5a91ba18ab9e6bf73a6e54ca4bca4f75b16c7e46240983a5f22def3","sha256:7fde5ab4c8f4042efcccdc0ad231958fd77d537861ef3672a25fc08ef7fa76e9"],"state_sha256":"0f4f01184c47c28ef98eb0aef2a0a4d425758b4c8772ec4c4d83dcf2a86b2545"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sTQBRWK6GgfMT+l3sDhDHGbWVufVJ6sLHsygbKktLqutxx+FiAsud1NpTFGXVfe6qzFvdBvPfI7LTyyPMkl3CA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-28T02:57:00.307274Z","bundle_sha256":"0943cab83af34f0728cef62b9f7475225e04f48aaa019d0f0348fa4c84ad56c2"}}